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Jiang H, Harrington D, Raby BA, Bertram L, Blacker D, Weiss ST, Lange C. Family-based association test for time-to-onset data with time-dependent differences between the hazard functions.
This proves that the proportionality assumption between the hazard functions λ13 and λ23 in model J does not match the data.
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The relation between the hazard function and the covariates was modeled by Cox's proportional-hazard regression.
First, there is a multiplicative relationship between the hazard function and the log-linear function of covariates.
The association between the hazard function and the explanatory variables was analysed by using a modification of Cox proportional hazards regression models.
Also, it assumes a log-linear relationship between the hazard function and the time and any number of metric and/or nonmetric variables.
Since the proportional hazards regression is dependent of proportionality between the hazard function of those exposed and those not exposed, the hazard functions across the follow-up period were calculated separately for men and women with the SAS procedure 'Life-test' providing tabulated and plotted hazards levels for exposed and unexposed groups.
Second, a Cox regression model was built between the hazard function of MetS and the extracted factors in 1,565 subjects in the cohort study design: h(t) = h0 t)exp(β0age + β1F1 + β2F2 + … + βkFk), and a MSP was developed by MSP = β1F1 + β2F2 + … + βkFk.
These differences in the hazard functions between models have to be taken into account when using a birth death process for modeling duplicate retention.
This reflects the advantage of our method and possibly the limitation of the diffusion approximation, which assumes that the values of the hazard functions are approximately constants between two observation/latent states.
Figure 6 shows the hazard functions.
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